Deposition of Externally Introduced Particles

Three distinct permeability damage mechanisms are analyzed for a given injection fluid rate and particle concentration. Particles are retained mainly in the thin core section near the inlet face. In this region the concentration of the flowing phase is assumed the same as the injected fluid (i.e., pp/ - ( P p f ) . ). Gradual pore reduction by surface deposition occurs when the particles of the injected suspension are smaller than the pore constrictions. Assume
that the surface deposition is the dominant mechanism compared to the entrainment, that is, kr»ke.

Single pore blocking occurs when the size of the particles in the injected fluid are comparable or bigger than the size of the pore constrictions. A substitution of Eqs. 10-12, 13, and 14 into Eq. 10-28 yields the following diagnostic equation:

Cake formation near the inlet face of the porous media occurs when the particles in the injected solutions are large relative to the pore size and at high a concentration. Combining Eqs. 10-22 and 17 yields the following diagnostic equation:

Mobilization and Subsequent Deposition of Indigeneous Particles

This case deals with the injection of a clear (particle free) solution into a porous media. A core is visualized as having two sections designated as the inlet and outlet sides. The particles of the porous media entrained by the flowing phase in the inlet part are recaptured and deposited at the outlet side of the core. Near the inlet port, the mobilization and entrainment of particles by the flowing phase is assumed to be the dominant mechanism compared to the particles retention (i.e., ke » kr}. Thus, dropping the particle retention term, Eqs. 10-35 and 36 yield the following solution for the mass of particles remaining on the pore surface

Depending on the particle concentration and size of the flowing phase entering the core, the outlet side diagnostic equations for three permeability
damage mechanisms mentioned previously are derived next.

Gradual Pore Reduction by Surface Deposition and Sweeping

Assume that the mass of the indigeneous or previously deposited particles on the pore surface is m*. Then, the area occupied by these particles is given by Eq. 10-29 as

Afg denotes the open flow area when all the deposits are removed. If simultaneous, gradual pore surface deposition and sweeping ar occurring near the outlet region, then both the entrainment and retention terms are considered equally important. Thus, substituting Eq. 10-46, Eq. 10-35 yields the following ordinary differential equation:

If only gradual surface deposition is taking place in the outlet region, then kr » ke . Therefore, dropping the particle retention term and substituting Eq. 10-46, Eqs. 10-35 and 36 for mpg = 0 are solved to obtain the amount of particles retained as:

Civan, F. "Modeling and Simulation of Formation Damage by Organic Deposition," Proceedings of the First International Symposium on Colloid Chemistry in Oil Production: Asphaltenes and Wax Deposition, ISCOP'95, Rio de Janeiro, Brazil, November 26-29, 1995, pp. 102-107.